### Home > APCALC > Chapter 7 > Lesson 7.3.3 > Problem7-130

7-130.

Integrate.

1. $\int \cos(x) \sin^2(x)dx$

Let $u = \sin(x)$.

1. $\int −\cos(3x − 2)dx$

$k\sin(3x − 2) + C$
What is $k$?

1. $\int x^{-4}e^{x^{-3}}dx$

Use $u$-substitution. Be careful choosing $u$.
Who has the higher power: $x^{−3}$ or $x^{−4}$?

1. $\int ( e ^ { 7 x - 2 } - \sqrt { 5 x } ) d x$

Before integrating, rewrite the square root term in the integrand with a fractional exponent.

1. $\int 2 \ln(4x)dx$

$\text{Recall that: }\int \ln(x)dx=x\ln(x)-x+C$

1. $\int \frac { 9 } { 9 + x } d x$

$9\int \frac{1}{9+x}dx$